(4x^2-x)(6x-2)=0

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Solution for (4x^2-x)(6x-2)=0 equation: 


Simplifying
(4x2 + -1x)(6x + -2) = 0

Reorder the terms:
(-1x + 4x2)(6x + -2) = 0

Reorder the terms:
(-1x + 4x2)(-2 + 6x) = 0

Multiply (-1x + 4x2) * (-2 + 6x)
(-1x * (-2 + 6x) + 4x2 * (-2 + 6x)) = 0
((-2 * -1x + 6x * -1x) + 4x2 * (-2 + 6x)) = 0
((2x + -6x2) + 4x2 * (-2 + 6x)) = 0
(2x + -6x2 + (-2 * 4x2 + 6x * 4x2)) = 0
(2x + -6x2 + (-8x2 + 24x3)) = 0

Combine like terms: -6x2 + -8x2 = -14x2
(2x + -14x2 + 24x3) = 0

Solving
2x + -14x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -7x + 12x2) = 0

Factor a trinomial.
2x((1 + -4x)(1 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, 0.25, 0.3333333333}

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